CN109816590A - Image extrapolation process method - Google Patents
Image extrapolation process method Download PDFInfo
- Publication number
- CN109816590A CN109816590A CN201811598972.XA CN201811598972A CN109816590A CN 109816590 A CN109816590 A CN 109816590A CN 201811598972 A CN201811598972 A CN 201811598972A CN 109816590 A CN109816590 A CN 109816590A
- Authority
- CN
- China
- Prior art keywords
- image
- interpolation
- matrix
- pixel
- dimension
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Landscapes
- Image Processing (AREA)
Abstract
Image extrapolation process method, determine the coordinate variable of image, the known function point of interpolation frame, construct generalized circular matrix, vandermonde vector space, the inner product calculated between subspace base vector obtains the metric tensor of subspace, matrix inversion method obtains the metric tensor of the dual spaces of subspace, the base that dual spaces are obtained by matrix operation, obtains the pseudo inverse matrix of generalized circular matrix for the basic matrix transposition of dual spaces.Determine the position in interpolation frame point for being inserted section；The generalized circular matrix having with the same item number of interpolation frame is obtained according to the abscissa of insertion point set.The generalized circular matrix for being inserted into point set is obtained into extrapolation matrix multiplied by pseudo inverse matrix.The pixel value that new pixel is obtained according to extrapolation matrix converts dimension in one dimension of image pixel by the mobile single-frame interpolation of pixel compartments, completes another dimension interpolation after image conversion dimension, until completing whole interpolation.Keep image more acurrate lively, is conducive to scientific research exploration, the imaging that public security is solved a case with military surveillance.
Description
Technical field
The present embodiments relate to technical field of image processing, and in particular to a kind of image extrapolation process method.
Background technique
It is high that the software (such as IrfanView) that existing interpolation technique is prevalent in the image procossing of profession neutralizes computer
In the image processing toolbox of grade language (the Image Processing Toolbox of such as Matlab language).
For IrfanView, although can not really know its source code, there is interpolation twice in the process of running and put
Greatly, since interpolation method itself destroys the property of the intrinsic module in two-dimentional Euclidean plane, after first time interpolation amplification
Pixel outer is clearly present in the image after second of interpolation amplification, increases new noise.In IrfanView operational process
In interdepended due to two variable of x, y, will appear the twill noise of diagonal line style after interpolation amplification twice, while also destroying two
Tie up the property of the intrinsic module in Euclidean plane.Further, since the technical costs that IrfanView is used is high, businessman for
The considerations of economic interests, interpolated amplified picture cannot deposit in operational process.
In the specification of high-level [computer Matlab and in other information summarized, linear interpolation is commonly used
Most coarse interpolation method, and most accurate interpolation is exactly that two arguments cube (Bi-Cubic) in 16 pixel grids are polynomial
Interpolation, although bidimensional can simultaneously interpolation, destroy abelian group characteristic simple and easy.
It is mentioned in existing image processing literature when inserting pixel with interpolation method, is mostly the repairing for locality, or be
Amplify figure and uses.Large area be improve tens times of hundred times of picture precision increase pixel technical solution there is no.
Lagrange's interpolation only provides the interpolation coefficient of several low orders in existing mathematical textbooks and handbook, and interpolation is not
It is good.Therefore a kind of new image processing techniques scheme is needed.
Summary of the invention
For this purpose, the embodiment of the present invention provides a kind of image extrapolation process method, it can be used for image procossing and video image
Processing makes image become more acurrate, more lively, more see clearly autumn hair, more show clues and traces, is more advantageous to scientific research exploration, public security
The imaging solved a case with military surveillance.
To achieve the goals above, the embodiment of the present invention provides the following technical solutions: a kind of image extrapolation process method, packet
It includes:
1) sequence and coordinate system of the coordinate variable of image are determined；
2) it is determined as n+1 known function point of interpolation frame, the known function point includes known coordinate point and
Know functional value, wherein n is order；
3) generalized circular matrix V is constructed by the known function point1；
4) the generalized circular matrix V is used1N+1 row as row vector constitute m dimension vandermonde vector space, the row
Vector is that the base for the n+1 n-dimensional subspace n that m ties up vandermonde vector space is denoted as e0, e1..., en, generalized circular matrix is denoted as V1=(e0,
e1..., en), wherein m is more than or equal to n+1, and m, n are natural number；
5) inner product calculated between the subspace base vector obtains the metric tensor g of subspaceij=ei*ej；
6) the metric tensor g of the dual spaces of the subspace is obtained by matrix inversion methodij *, the dual spaces
Matrix is the inverse matrix of the metric tensor of the subspace, i.e. (gij *)=(gij)-1；
7) base of the dual spaces is obtained by matrix operation, the base of the dual spaces is (e0, e1..., en)=
(e0, e1..., en)(gij *)；
8) basic matrix of dual spaces is subjected to transposition and obtains the pseudo inverse matrix V of generalized circular matrix1 -1, i.e. V1 -1=(e0,
e1..., en)T, wherein T represents the transposition operation of matrix；
9) position in n+1 point of interpolation frame for being inserted section is determined；
10) number for giving insertion point between adjacent two pixel is inserted into d-1 new pixels, wherein d between adjacent two pixel
Insertion point is represented to the isodisperse in insertion section；
11) abscissa of insertion point set is determined；
12) the generalized circular matrix V having with the same item number of interpolation frame is obtained according to the abscissa of insertion point set2；
13) the extrapolation matrix E of (d-1) × (n+1) is constructeddn；
14) according to the extrapolation matrix EdnObtain the pixel value z of d-1 new pixelsi, wherein i=1 ..., d-1；
15) Interpolating transform g (x)=G (f (x)) is constructed, wherein f (x) is one-dimensional variable function, and g (x) is obtained after interpolation
Function；
16) in a dimension of image pixel since the first row or first row, in the first row or first row forward
By the mobile single-frame interpolation of pixel compartments；
17) next line or next column of image pixel are changed to, step 16) is repeated and completes next line or next column interpolation, instead
Step 16) is executed again and step 17) completes pixel last line interpolation of the image in corresponding dimension；
18) it is transformed into another dimension, another dimension after repeating step 16) and step 17) completion image conversion dimension is inserted
Value, until completing image whole interpolation.
As the preferred embodiment of image extrapolation process method, described image is two dimensional image, 3-D image or dimensional images,
The dimension of dimensional images is greater than three-dimensional.
As the preferred embodiment of image extrapolation process method, in the step 2), the known function value uses image slices
The gray value of vegetarian refreshments；The coefficient of interpolation polynomial is constructed by the known function value；
The known function value is by the way that being inserted, function is calculated or previously given mode obtains.
As the preferred embodiment of image extrapolation process method, in the step 9), there is n section in n+1 point, when n is
When odd number, there are center sections in n section.
As the preferred embodiment of image extrapolation process method, in the step 13), the formula of extrapolation matrix is Edn=V2V1 -1。
As the preferred embodiment of image extrapolation process method, using pixel rice transplanter to d-1 new pictures in the step 14)
The pixel value z of vegetarian refreshmentsiIt is calculated；
This formula is z=EdnY, this is the original place interpolation component of pixel rice transplanter；
Wherein z=(z1..., zd-1)
Y=(y1..., yn+1)
Y is the coordinate variable of image.
As the preferred embodiment of image extrapolation process method, in the step 16), pixel tripping original for image
Without interpolation, or in original pixel point position again interpolation；
By Interpolating transform g (x)=G (f (x)) make interpolating matrix in same a line or same row it is single-frame mobile forward until
The last one pixel.Because there is locomotive function, Interpolating transform g (x)=G (f (x)) is exactly our so-called pixel rice transplanters.
It further include step 19) for color image as the preferred embodiment of image extrapolation process method,
Step 19): it is gradually complete according to the component sequence of color image that step 16), step 17) and step 18) are repeated
At interpolation.
As the preferred embodiment of image extrapolation process method, for dimensional images, repeat step 16), step 17),
Step 18) and step 19) are sequentially completed the interpolation of dimensional images by dimension.
The embodiment of the present invention, which has the advantages that, can be used for two dimension, three-dimensional and higher-dimension image procossing, two step interpolation etc.
Valence can't see the trace noise of first time interpolation after a step interpolation, second of interpolation, since each dimension interpolation independently carries out,
One-dimensional interpolation method is convenient to complete to appoint by the twill noise not having after dimension interpolation between different dimensional, one-dimensional interpolation method by dimension interpolation
What data of dimension and interpolation of figure can make image become more acurrate, more lively, more see clearly autumn hair, more show spider's thread horse
Mark is conducive to scientific research exploration, the imaging that public security is solved a case with military surveillance, improves the treatment effect of image, so that interpolation image
Processing becomes more accurate, more acurrate, is easier.
Detailed description of the invention
It, below will be to embodiment party in order to illustrate more clearly of embodiments of the present invention or technical solution in the prior art
Formula or attached drawing needed to be used in the description of the prior art are briefly described.It should be evident that the accompanying drawings in the following description is only
It is merely exemplary, it for those of ordinary skill in the art, without creative efforts, can also basis
The attached drawing of offer, which is extended, obtains other implementation attached drawings.
L65, E65, E83, E85 involved in the technical program represent the label of interpolation series are as follows:
L65: 5 rank multinomial interpolation of Lagrange's interpolation 6 etc. point；
E65: the pseudo- 5 rank multinomial interpolation of extrapolation 6 etc. point；
E83: the pseudo- 3 rank multinomial interpolation of extrapolation 8 etc. point；
E85: the pseudo- 5 rank multinomial interpolation of extrapolation 8 etc. point, other the rest may be inferred.
Fig. 1 is the image extrapolation process method flow schematic diagram provided in the embodiment of the present invention；
Fig. 2 is the image extrapolation process method and step S19 schematic diagram provided in the embodiment of the present invention；
Fig. 3 is the image extrapolation process method and step S20 schematic diagram provided in the embodiment of the present invention；
Fig. 4 is that the black and white provided in the embodiment of the present invention shines treatment effect contrast schematic diagram；
Fig. 5 is the imaging results contrast schematic diagram for keeping smile more magnificent provided in the embodiment of the present invention；
Fig. 6 is the street corner dancing girl's photo schematic diagram provided in the embodiment of the present invention；
Fig. 7 is original image of the small bright hole by amplification in the street corner dancing girl's photo provided in the embodiment of the present invention；
Fig. 8 is 5 order polynomials provided in the embodiment of the present invention between the Lagrange's interpolation street corner of 6 equal parts center
Small bright hole pattern in dancing girl's photo；
Fig. 9 is that the use extrapolation provided in the embodiment of the present invention is worked as containing higher-order function item to x10When street corner dancing girl shine
The medium and small bright hole pattern of piece；
Figure 10 is that the green laser provided in the embodiment of the present invention injects indoor figure from the outdoor peep hole by door；
Figure 11 be the embodiment of the present invention in provide injection it is indoor round aperture amplification and screenshot formed about aperture
Low pixel number figure；
Figure 12 is the indoor aperture image L65 interpolation of injection that provides treated figure in the embodiment of the present invention；
Figure 13 is that the indoor aperture image of injection provided in the embodiment of the present invention passes through x using the technical program0...,
x10Figure after the E65 extrapolation process of item；
Figure 14 is that the indoor aperture image of injection provided in the embodiment of the present invention passes through x using the technical program0...,
x10Figure after the E83 extrapolation process of item；
Figure 15 is that the indoor aperture image of injection provided in the embodiment of the present invention passes through x using the technical program0...,
x12Figure after the E85 extrapolation process of item；
Figure 16 is the ghost image figure of the sunlit eaves lower edge provided in the embodiment of the present invention.
Specific embodiment
Embodiments of the present invention are illustrated by particular specific embodiment below, those skilled in the art can be by this explanation
Content disclosed by book is understood other advantages and efficacy of the present invention easily, it is clear that described embodiment is the present invention one
Section Example, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art are not doing
Every other embodiment obtained under the premise of creative work out, shall fall within the protection scope of the present invention.
The technical program uses following theoretical basis:
General geometric space can all be described with Lie group and Lie Algebraic Structure.The basic structure of Lie group is per one-dimensional list
Lie group is tieed up, its generation member is the tangent vector of one-dimensional curve, constitutes corresponding Lie algebra member.One-dimensional interpolation is inserted by dimension is complete again,
Greatly remain the exchangeability of the abelian group for the two-dimentional commutative Lie algebra being made of one-dimensional Lie algebra.
Theoretical physicist and applied mathematician Guo Dong rise the first interpolation theorem of Guo Shi proposed.
Theorem 1: it constitutes by x=x0, x1..., xnThe n+1 of the inverse matrix of vandermonde square array that generates of n+1 point
Column vector is the respective coefficient vector of Lagrange interpolation polynomial in these points.
It is calculated as parallel computation and simple and feasible using what this theorem made Lagrange interpolation polynomial coefficient, into
And Lagrange Polynomial interpolating method is made to become simple and feasible in the calculating of scientific numerical value.It is fixed using above-mentioned the first interpolation of Guo Shi
Reason can make computational accuracy improve 10,000,000,000 (10 when research calculates many electron atoms orbital wave function10) times effect.
The interpolation and extrapolation of Lagrange's interpolation all can be by being realized based on the first interpolation theorem of Guo Shi and being referred to as Guo Shi
Interpolation method, traditional extrapolation is not departing from the function subspace where interpolation method.For having exceeded original function subspace
Interpolation method is then known as Guo Shi extrapolation, and theory narrative is then the second interpolation theorem of Guo Shi.
Theorem 2: it constitutes by x=x0, x1..., xnThe vandermonde Rectangular Matrix (columns m >=n+1) that generates of n+1 point
N+1 column vector of pseudo inverse matrix is the respective coefficient vector of extrapolation multinomial in these points.
On the x-y plane, it is known that n+1 x value: x=x0, x1..., xnLocate corresponding n+1 y value y0, y1..., yn,
It is gone to determine unique m (m >=n+1) order polynomial with pseudo-inverse matrix method according to theorem 2.As m=n+1, theorem 1 is returned to
The classical Lagrange's interpolation of description.And the emphasis of extrapolation and the case where be m > n+1 to the breakthrough of classical theory.This
It is the core of technical solution of the present invention theory.
Above-mentioned way be it is pioneering, change it is Euclidian it is eternal without exception: " can be uniquely determined between two o'clock one it is straight
Line ", and a parabola, cube curve cannot be uniquely determined, a high order curve can not be uniquely determined.Euclid
The popularization version of axiom is that n+1 point in plane can uniquely determine a n-order polynomial curve, and classical glug is bright
The basis of day interpolation polynomial theory.Technical solution of the present invention breaks through the limitation of conventional solution, for n+1 given letter
The point of numerical value, we can uniquely determine the luminance curve of an arbitrary order.
The technical solution of the embodiment of the present invention is based on above-mentioned theoretical basis.
Specifically, providing a kind of image extrapolation process method referring to Fig. 1, comprising the following steps:
S1: the sequence and coordinate system of the coordinate variable of image are determined；
S2: being determined as n+1 known function point of interpolation frame, and the known function point includes known coordinate point and
Know functional value, wherein n is order；
S3: generalized circular matrix V is constructed by the known function point1；
S4: the generalized circular matrix V is used1N+1 row as row vector constitute m dimension vandermonde vector space, it is described
Row vector is that the base for the n+1 n-dimensional subspace n that m ties up vandermonde vector space is denoted as e0, e1..., en, generalized circular matrix is denoted as V1=
(e0, e1..., en), wherein m is more than or equal to n+1, and m, n are natural number；
S5: it calculates the inner product between the subspace base vector and obtains the metric tensor g of subspaceij=ei·ej；
S6: the metric tensor g of the dual spaces of the subspace is obtained by matrix inversion methodij *, the dual spaces
Matrix is the inverse matrix of the metric tensor of the subspace, i.e. (gij *)=(gij)-1；
S7: obtaining the base of the dual spaces by matrix operation, and the base of the dual spaces is (e0, e1..., en)=
(e0, e1..., en)(gij *)；
S8: the basic matrixs of dual spaces is subjected to transposition and obtains having a size of m × pseudo inverse matrix the V of (n+1)1 -1, i.e. V1 -1=
(e0, e1..., en)T, wherein T represents the transposition operation of matrix；
S9: the position in n+1 point of interpolation frame for being inserted section is determined；
S10: giving the number of insertion point between adjacent two pixel, and d-1 new pixels are inserted between adjacent two pixel, wherein
D represents insertion point to the isodisperse in insertion section；
S11: the abscissa of insertion point set is determined；
S12: the generalized circular matrix V having with the same item number of interpolation frame is obtained according to the abscissa of insertion point set2；
S13: the extrapolation matrix E of construction (d-1) × (n+1)dn；
S14: according to the extrapolation matrix EdnObtain the pixel value z of d-1 new pixelsi, wherein i=1 ..., d-1；
S15: construction Interpolating transform g (x)=G (f (x)), wherein f (x) is one-dimensional variable function, and g (x) is obtained after interpolation
Function；
S16: in a dimension of image pixel since the first row or first row, in the first row or first row forward
By the mobile single-frame interpolation of pixel compartments；
S17: changing to the next line or next column of image pixel, repeats step S16 and completes next line or next column interpolation, instead
Step S16 and step S17 is executed again completes pixel last line interpolation of the image in corresponding dimension；
S18: being transformed into another dimension, and another dimension after repeating step S16 and step S17 completion image conversion dimension is inserted
Value, until completing image whole interpolation.
In one embodiment of image extrapolation process method, described image be two dimensional image, 3-D image or dimensional images,
The dimension of dimensional images is greater than three-dimensional.The sequence and coordinate system of the coordinate variable of image are determined in image extrapolation process method, such as
H-w (high-wide) or x-y (x coordinate-y-coordinate).Interpolation method is not limited to two dimensional image, can be any degree dimension image.As the four-dimension is schemed
As i.e. Spatial distributions image, coordinate can be asserted x-y-z-t.Due to using one-dimensional interpolation method, high space all can be all again for dimension
Dimension successively goes interpolation, does not interfere with each other.
In one embodiment of image extrapolation process method, in the step S2, the known function value uses image slices
The gray value of vegetarian refreshments；The coefficient of interpolation polynomial is constructed by the known function value；The known function value is by being inserted
Function calculates or previously given mode obtains.Such as n+1 known function point.It will be with the known letter of these known function points
Numerical value, to construct the coefficient of interpolation polynomial.The known function value of known function point can be by being inserted calculating for function
It is given in advance to being also possible to, such as the gray value of pixel.
In one embodiment of image extrapolation process method, in the step S9, there is n section in n+1 point, when n is
When odd number, there are center sections in n section.Such as n=0 be starting point, then between center be located at (n-1)/2 to (n+1)/2 it
Between.Such as it is then 3 that n+1, which is 4, n,；There are 3 sections between 4 points, (n-1)/2=1, (n+1)/2=2 are located at n=1 and n between center
Between=2.If n is even number, there is 2 centers section, interpolation should be in n/2-1 to n/2, two section n/2 to n/2+1.
In one embodiment of image extrapolation process method, in the step S13, the formula of extrapolation matrix is Edn=V2V1 -1.Using pixel rice transplanter to the pixel value z of d-1 new pixels in the step S14iIt is calculated；
This formula is z=EdnY, this is the original place interpolation component of pixel rice transplanter；
Wherein z=(z1..., zd-1)
Y=(y1..., yn+1)
Y is the coordinate variable of image.Specifically, being a linear lattice between for example two neighboring pixel, d is divided into after interpolation
Part (is exactly that a plane grid becomes d for 2-d plane graph2A plane grid.It will d-1 new pixels of insertion between two pixels
Point.For image, two dimensional image is exactly two-dimentional field, and extrapolation matrix is exactly pixel rice transplanter as you were, itself is first
It is n that tail, which subtracts each other length, width 1, and original pixel plays the role of determining row and arrange surely and the reference of definite value.
Specifically, one is counted to a several corresponding relationship and is known as function, the corresponding relationship of a function a to function
Referred to as convert.F (x) is the function of an one-dimensional variable, and for example certain in two-dimension picture is one-dimensional, and independent variable x is exactly the position of pixel
Serial number is set, domain is 1 to N.Since interpolation is carried out by dimension, does not need to consider multidimensional while slotting problem, g (x) are
The function obtained after interpolation will be inserted into d-1 point between two pixels, this is that the domain of new function is 1 to d (N-1)+1.For
Do not have the pixel value f (i) of the ith pixel of interpolation, can be used to+1 pixel value g (d (i- of d (i-1) for defining new primitive definition
1)+1)=f (i).
In one embodiment of image extrapolation process method, in the step S16, pixel tripping original for image
Without interpolation, or in original pixel point position again interpolation；Make interpolating matrix same by Interpolating transform g (x)=G (f (x))
It is single-frame mobile until the last one pixel forward in capable or same row.Because there is locomotive function, Interpolating transform g (x)=G (f
(x)) it is exactly our so-called pixel rice transplanters.
Specifically, can not insert with tripping for original pixel, the corresponding position weight for being inserted in original pixel again can also be put down
Existing initial value.Interpolating transform g (x)=G (f (x)) seems that the pixel rice transplanter put on a moving belt makes matrix of differences in same a line
It is single-frame mobile until the last one pixel forward.
It further include step S19 for color image in one embodiment of image extrapolation process method,
Step S19: it is gradually complete according to the component sequence of color image that step S16, step S17 and step S18 are repeated
At interpolation.For color image, it is respectively a two dimensional image that there are three components R, G and B for color dimension, can by step S16, S17,
S18 is gradually completed according to component sequence.
It further include step S20 for dimensional images, step S20 is repeated in one embodiment of image extrapolation process method
Step S16, step S17, step S18 and step S19 are executed, the interpolation of dimensional images is sequentially completed by dimension.
The practice effect of technical solution in the embodiment of the present invention is illustrated below.
Referring to fig. 4, technical solution in the embodiment of the present invention is applied to the processing that black and white is shone.Picture is taken from Matlab
An exemplary criteria shine, the head of entitled Lena shines.In order to show the function of different interpolation methods, the side of Lena cap is carried out
Amplification.Top figure is amplified original image in Fig. 4, due to the low visible pixels grid of pixel number.Middle graph in Fig. 4 uses four
The interpolation method of 8x8 based on Lagrangian cubic polynomial between point, the function base of interpolation are 1, x, x2, x3, image becomes smooth company
It is continuous.The figure of bottom has used the function space of the 8x8 between 4 points based on technical solution of the present invention to insert method, the letter of interpolation in Fig. 4
Base is x0..., x6, the cap lines in image becomes apparent from.
Referring to Fig. 5, the imaging for keeping beauty smile more magnificent using technical solution in the embodiment of the present invention.Top figure in Fig. 5
It is the low pixel number picture obtained by partial enlargement, examines it can be seen that discontinuity caused by pixel grid.In Fig. 5
Middle graph using the interpolation method of the 8x8 based on Lagrangian cubic polynomial between 4 points, the function base of interpolation is 1, x, x2, x3,
Image becomes smooth continuous.The figure of bottom inserts method using the function space of the 8x8 between 4 points in Fig. 5, and the function base of interpolation is
x0..., x7, high priest is the personage of a performance in image, and the personage smile is more bright than original image and interpolation method interpolation
It is rotten, and everyone facial expression all becomes more lively.This is because higher-order function base can highlight between adjacent pixels
Change in rain.And these variations are to have been smoothed out in Lagrange's interpolation.
Known, natural light through small holes can produce Fu Langhefu (Frainhofer) diffraction, and this is originally the light in nature
Learn effect.Can be disclosed during handling live photo by the technical program usually naked-eye observation less than subtle physics it is existing
As.For this purpose, design Laser Experiments, which carry out observation, confirms this physical phenomenon, if this shows the display screen of scientific research apparatus using this
The technical solution of invention can observe unexpected new effect.The military is scouted and the various telescopic systems of observation can be whereby
It was found that tiny target.The various evidence obtainings of the police and observation system can be found that new subtle clues and new evidence.
The following contents verifies the effect of the technical solution processing live photo of the present embodiment.
It is the photo of street corner dancing girl, number of pixels is accurately 1720 × 2293 × 3=11831880 referring to Fig. 6.From left to right
There are two small bright holes for the overhead of 4th personage.Fig. 7 is original image of the small bright hole by amplification, it can be seen that rectangular pixel side
Lattice.Because amplifying the new picture of screenshot becomes the picture of low pixel number.Two unthreaded holes show pixel grid in figure, in addition to this simultaneously
Without other abnormal.
The bright between the glug of 6 equal parts center of 5 order polynomials is done with the point (5 sections) of 6 known function values
Day interpolation, referring to Fig. 8, figure becomes smooth, but has no new phenomenon appearance.
Worked as by extrapolation containing higher-order function item to x referring to Fig. 9 using the technical solution of the present embodiment10When, occur
It is unexpected that technical effect showed circular aperture outside circular unthreaded hole.This is exactly optical diffraction fringe, in optics
Referred to as Fu Langhefu (Fraunhofer) diffraction.
In order to ensure the above-mentioned circular aperture striped imaged by the technical program is Fu Langhefu optical diffraction,
Continue design Laser Experiments and carrys out repeated authentication.It is to inject room from the outdoor peep hole by door with green laser referring to Figure 10
Interior, another people takes the whole picture of door for 4-5 meters indoors at a distance.Figure 11 is round aperture amplification and screenshot is formed about aperture
Low pixel number picture, pixel square is obvious.Figure 12 is to the L65 interpolation method processing result of aperture image, and figure is smooth but simultaneously
Do not highlight diffraction fringe.Figure 13 is to pass through x using the technical program0..., x10The E65 extrapolation processing of item, Fu Langhefu diffraction
Credit is so on screen.Figure 14 is to pass through x using the technical program0..., x10E83 extrapolation process as a result, Fu Langhefu optics spreads out
It is more obvious to penetrate striped.Figure 15 is to pass through x using the technical program0..., x12The E85 extrapolation processing of item, Fu Langhefu diffraction
Show nothing left fully.
The understanding that Fu Langhefu optical diffraction can be shown by the technical program is sunlit eaves referring to Figure 16
The ghost image of lower edge, the concrete reason of ghost image are explained still as Fu Langhefu optical diffraction.Therefore based on above-mentioned verifying, skill of the present invention
Art scheme can make that image is finer, character face's expression is more lively by having the extrapolation of nearly higher order term, be suitble to processing life
Photo and video and portrait photographs and video.Extrapolation with remote higher order term can show that figure is subtle and variation in rain,
Autumn hair is seen clearly, shows clues and traces fully, is suitable for Science Explorations, public security is solved a case, the figure in the fields such as military surveillance and the place of video
Reason.
Although above having used general explanation and specific embodiment, the present invention is described in detail, at this
On the basis of invention, it can be made some modifications or improvements, this will be apparent to those skilled in the art.Therefore,
These modifications or improvements without departing from theon the basis of the spirit of the present invention are fallen within the scope of the claimed invention.
Claims (9)
1. image extrapolation process method characterized by comprising
1) sequence and coordinate system of the coordinate variable of image are determined；
2) it is determined as n+1 known function point of interpolation frame, the known function point includes known coordinate point and known letter
Numerical value, wherein n is order；
3) generalized circular matrix V is constructed by the known function point1；
4) the generalized circular matrix V is used1N+1 row as row vector constitute m dimension vandermonde vector space, the row vector
E is denoted as the m base for tieing up the n+1 n-dimensional subspace n of vandermonde vector space0, e1..., en, generalized circular matrix is denoted as V1=(e0,
e1..., en), wherein m is more than or equal to n+1, and m, n are natural number；
5) inner product calculated between the subspace base vector obtains the metric tensor g of subspaceij=ei·ej；
6) the metric tensor g of the dual spaces of the subspace is obtained by matrix inversion methodij *, the matrix of the dual spaces
For the inverse matrix of the metric tensor of the subspace, i.e. (gij *)=(gij)-1；
7) base of the dual spaces is obtained by matrix operation, the base of the dual spaces is (e0, e1..., en)=(e0,
e1..., en)(gij *)；
8) basic matrix of dual spaces is subjected to transposition and obtains the pseudo inverse matrix V of generalized circular matrix1 -1, i.e. V1 -1=(e0, e1...,
en)T, wherein T represents the transposition operation of matrix；
9) position in n+1 point of interpolation frame for being inserted section is determined；
10) number for giving insertion point between adjacent two pixel is inserted into d-1 new pixels between adjacent two pixel, and wherein d is represented
Isodisperse of the insertion point to insertion section；
11) abscissa of insertion point set is determined；
12) the generalized circular matrix V having with the same item number of interpolation frame is obtained according to the abscissa of insertion point set2；
13) the extrapolation matrix E of (d-1) × (n+1) is constructeddn；
14) according to the extrapolation matrix EdnObtain the pixel value z of d-1 new pixelsi, wherein i=1 ..., d-1；
15) Interpolating transform g (x)=G (f (x)) is constructed, wherein f (x) is one-dimensional variable function, and g (x) is the letter obtained after interpolation
Number；
16) in a dimension of image pixel since the first row or first row, picture is pressed forward in the first row or first row
The mobile single-frame interpolation of plain lattice；
17) next line or next column of image pixel are changed to, step 16) is repeated and completes next line or next column interpolation, hold repeatedly
Row step 16) and step 17) complete pixel last line interpolation of the image in corresponding dimension；
18) it is transformed into another dimension, step 16) is repeated and step 17) completes another dimension interpolation after image conversion dimension, directly
To completion image whole interpolation.
2. image extrapolation process method according to claim 1, which is characterized in that described image is two dimensional image, three-dimensional
The dimension of image or dimensional images, dimensional images is greater than three-dimensional.
3. image extrapolation process method according to claim 1, which is characterized in that in the step 2), the known letter
Numerical value uses the gray value of image slices vegetarian refreshments；The coefficient of interpolation polynomial is constructed by the known function value；
The known function value is by the way that being inserted, function is calculated or previously given mode obtains.
4. image extrapolation process method according to claim 1, which is characterized in that in the step 9), have in n+1 point
N section, when n is odd number, there are center sections in n section.
5. image extrapolation process method according to claim 1, which is characterized in that in the step 13), extrapolation matrix
Formula is Edn=V2V1 -1。
6. image extrapolation process method according to claim 1, which is characterized in that inserted in the step 14) using pixel
Pixel value z of the seedling machine to d-1 new pixelsiIt is calculated；
The original place interpolation component that the pixel rice transplanter uses is z=Edny；
Wherein z=(z1..., zd-1)
Y=(y1..., yn+1)
Y is the coordinate variable of image.
7. image extrapolation process method according to claim 6, which is characterized in that in the step 16), for image original
Some pixel trippings are without interpolation, or in original pixel point position again interpolation；
Keep interpolating matrix single-frame mobile until last forward in same a line or same row by Interpolating transform g (x)=G (f (x))
One pixel, the pixel rice transplanter refer to the appellation to Interpolating transform g (x)=G (f (x)).
8. image extrapolation process method according to claim 1, which is characterized in that further include step for color image
19),
Step 19): step 16), step 17) and step 18) are repeated and gradually completes to insert according to the component sequence of color image
Value.
9. image extrapolation process method according to claim 8, which is characterized in that for dimensional images, repeat step
It is rapid 16), step 17), step 18) and step 19), the interpolation of dimensional images is sequentially completed by dimension.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811598972.XA CN109816590B (en) | 2018-12-26 | 2018-12-26 | Image extrapolation processing method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811598972.XA CN109816590B (en) | 2018-12-26 | 2018-12-26 | Image extrapolation processing method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109816590A true CN109816590A (en) | 2019-05-28 |
| CN109816590B CN109816590B (en) | 2023-03-14 |
Family
ID=66602365
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811598972.XA Active CN109816590B (en) | 2018-12-26 | 2018-12-26 | Image extrapolation processing method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109816590B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112364319A (en) * | 2020-10-12 | 2021-02-12 | 西安电子科技大学 | Biological characteristic template protection method and device based on binary tree shuffling |
Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005062196A2 (en) * | 2003-12-11 | 2005-07-07 | Geoenergy, Inc. | Method and apparatus for efficient data acquisition and interpolation |
| US20070070424A1 (en) * | 2005-09-16 | 2007-03-29 | Fuji Photo Film Co., Ltd. | Image processing method and image recording apparatus |
| CN101056417A (en) * | 2006-04-10 | 2007-10-17 | 三菱电机株式会社 | Image processing apparatus, image processing method, image output apparatus, and image processing system |
| CN201084028Y (en) * | 2007-09-25 | 2008-07-09 | 薛玉起 | Electric heating type floor heating device automatic temperature control device |
| CN101436250A (en) * | 2008-11-19 | 2009-05-20 | 西安电子科技大学 | Multi-view angle human face recognizing method based on non-linear tensor resolution and view angle manifold |
| WO2009076816A1 (en) * | 2007-12-17 | 2009-06-25 | Huawei Technologies Co., Ltd. | Digital image interpolating method and device |
| CN101626512A (en) * | 2009-08-11 | 2010-01-13 | 北京交通大学 | Method and device of multiple description video coding based on relevance optimization rule |
| CN102521794A (en) * | 2011-11-10 | 2012-06-27 | 广东威创视讯科技股份有限公司 | Image interpolation method and device based on spline surface |
| CN103530529A (en) * | 2013-11-01 | 2014-01-22 | 上海无线电设备研究所 | Massive target performance data fast reading and precise interpolation method |
| CN104915609A (en) * | 2015-05-28 | 2015-09-16 | 武汉科技大学 | Data hiding method based on Lagrange interpolation method and multiple clouds |
| EP3276577A1 (en) * | 2016-07-25 | 2018-01-31 | Technische Universität Berlin | Hölder adaptive image synthesis |
-
2018
- 2018-12-26 CN CN201811598972.XA patent/CN109816590B/en active Active
Patent Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005062196A2 (en) * | 2003-12-11 | 2005-07-07 | Geoenergy, Inc. | Method and apparatus for efficient data acquisition and interpolation |
| US20070070424A1 (en) * | 2005-09-16 | 2007-03-29 | Fuji Photo Film Co., Ltd. | Image processing method and image recording apparatus |
| CN101056417A (en) * | 2006-04-10 | 2007-10-17 | 三菱电机株式会社 | Image processing apparatus, image processing method, image output apparatus, and image processing system |
| CN201084028Y (en) * | 2007-09-25 | 2008-07-09 | 薛玉起 | Electric heating type floor heating device automatic temperature control device |
| WO2009076816A1 (en) * | 2007-12-17 | 2009-06-25 | Huawei Technologies Co., Ltd. | Digital image interpolating method and device |
| CN101436250A (en) * | 2008-11-19 | 2009-05-20 | 西安电子科技大学 | Multi-view angle human face recognizing method based on non-linear tensor resolution and view angle manifold |
| CN101626512A (en) * | 2009-08-11 | 2010-01-13 | 北京交通大学 | Method and device of multiple description video coding based on relevance optimization rule |
| CN102521794A (en) * | 2011-11-10 | 2012-06-27 | 广东威创视讯科技股份有限公司 | Image interpolation method and device based on spline surface |
| CN103530529A (en) * | 2013-11-01 | 2014-01-22 | 上海无线电设备研究所 | Massive target performance data fast reading and precise interpolation method |
| CN104915609A (en) * | 2015-05-28 | 2015-09-16 | 武汉科技大学 | Data hiding method based on Lagrange interpolation method and multiple clouds |
| EP3276577A1 (en) * | 2016-07-25 | 2018-01-31 | Technische Universität Berlin | Hölder adaptive image synthesis |
Non-Patent Citations (3)
| Title |
|---|
| GUI ZHIGUO .ETC: "Radiographic Image Enhancement Based on Lagrange Interpolation", 《SEMICONDUCTOR TECHNOLOGY》 * |
| WEN JUNHAI .ETC: "Method of reconstructing sectional image based on tomosynthesis and Vandermonde matrix", 《ACTA ELECTRONICA SINICA》 * |
| 刘强等: "海底地形数据网格化方法研究", 《舰船电子工程》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112364319A (en) * | 2020-10-12 | 2021-02-12 | 西安电子科技大学 | Biological characteristic template protection method and device based on binary tree shuffling |
| CN112364319B (en) * | 2020-10-12 | 2022-12-23 | 西安电子科技大学 | Biological characteristic template protection method and device based on binary tree shuffling |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109816590B (en) | 2023-03-14 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Wang et al. | LFNet: A novel bidirectional recurrent convolutional neural network for light-field image super-resolution | |
| Mann et al. | Video orbits of the projective group a simple approach to featureless estimation of parameters | |
| CN109416727B (en) | Method and device for removing glasses in face image | |
| Rahtu et al. | Affine invariant pattern recognition using multiscale autoconvolution | |
| CN108509848A (en) | The real-time detection method and system of three-dimension object | |
| Li et al. | Symmetrical feature propagation network for hyperspectral image super-resolution | |
| CN105120185A (en) | Image matting method and device for video images | |
| Yang et al. | Designing display pixel layouts for under-panel cameras | |
| CN110896467A (en) | Method and apparatus for restoring image | |
| Zhu et al. | Revisiting spatio-angular trade-off in light field cameras and extended applications in super-resolution | |
| CN109727196A (en) | Image interpolation processing method | |
| Zhang et al. | Imaging through the atmosphere using turbulence mitigation transformer | |
| Wang et al. | Transformer for 3D point clouds | |
| CN102156986A (en) | Calibration method of near-infrared camera | |
| Bujnák | Algebraic solutions to absolute pose problems | |
| Duan et al. | A new imaging model of Lytro light field camera and its calibration | |
| Chen et al. | Deep light field super-resolution using frequency domain analysis and semantic prior | |
| CN114758145A (en) | Image desensitization method and device, electronic equipment and storage medium | |
| CN109816590A (en) | Image extrapolation process method | |
| CN114463408A (en) | Free viewpoint image generation method, device, equipment and storage medium | |
| CN112132914B (en) | Image scale space establishment method and image processing chip | |
| CN114757822B (en) | Binocular-based human body three-dimensional key point detection method and system | |
| US9905020B2 (en) | Method and circuitry for performing census transforms | |
| Redlich et al. | An embedded hardware architecture for real-time super-resolution in infrared cameras | |
| WO2022247394A1 (en) | Image splicing method and apparatus, and storage medium and electronic device |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |